Magnetic field sensors can be used to sense an angle of rotation of a shaft or other object. For example, a magnet can be mounted on the shaft, and a magnetic field sensor can be arranged proximate the magnet in order to sense a magnetic field induced by the magnet as it rotates with the shaft. When the magnetic field sensor is mounted next to or adjacent the shaft, i.e., off of the axis of rotation of the shaft, the sensor is often referred to as an “off-axis” magnetic field angle sensor. Off-axis magnetic field angle sensors often are implemented when the end of the shaft is unavailable as a location for the sensor or there simply is not space available on the shaft. Generally, an “on-axis” magnetic field sensor, then, is one in which the sensor is mounted at or near the end of the shaft, generally in-line with or on the axis of rotation. In some embodiments, on-axis magnetic field angle sensors can comprise gradiometers, such that an on-axis magnetic field gradient sensor measures a gradient of the magnetic field on the rotation axis. The gradient can be measured in sufficient approximation in some applications by sampling the magnetic field at samplings points close to and on opposing sides of the axis and combining the samples, such as by subtraction.
In many applications there is a general preference for magnetic field angle sensors, whether off- or on-axis, to be inexpensive while also being robust with respect to external magnetic fields and other disturbances. A drawback of some conventional approaches, then, is a requirement of at least two sensor substrates with sensor elements having the same magnetic sensitivity and being highly linear. While some approaches address the linearity requirement by using Hall-effect sensor elements, there could be opportunities for other, non-Hall approaches if the linearity requirement were reduced or eliminated. Many conventional approaches use stronger and therefore more expensive magnets, which is another drawback when cost is a concern. Additionally, the accuracy of many conventional magnetic field angle sensors can be reduced if assembly tolerances are not closely controlled. Yet another drawback of many conventional on-axis magnetic field angle sensors is errors caused by background magnetic fields. In general, therefore, there are numerous drawbacks associated with conventional magnetic field angle sensors.